Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

What does the symbol '≥' represent in inequalities?

Back

'≥' means 'greater than or equal to'. It indicates that the value can be greater than or equal to a certain number.

Front

What does the symbol '>' represent in inequalities?

Back

'>' means 'greater than'. It indicates that the value must be strictly greater than a certain number.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dashed line indicates that the points on the line are not included (> or <).

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of the solution to a system of inequalities?

Back

The solution is represented by the shaded region on the graph where all inequalities overlap.

Front

What does it mean if a point lies above the line in a graph of an inequality?

Back

If a point lies above the line, it means that the point satisfies the inequality represented by that line (for 'greater than' inequalities).

Front

What does it mean if a point lies below the line in a graph of an inequality?

Back

If a point lies below the line, it means that the point satisfies the inequality represented by that line (for 'less than' inequalities).

Front

How do you graph the inequality y < 2x + 3?

Back

To graph y < 2x + 3, first graph the line y = 2x + 3 with a dashed line, then shade below the line.

Front

What is the boundary line in a system of inequalities?

Back

The boundary line is the line that represents the equality part of the inequalities. It divides the graph into two regions.